Noise-induced instability in self-consistent Monte Carlo calculations

We identify, analyze, and propose remedies for a numerical instability responsible for the growth or decay of sums that should be conserved in Monte Carlo simulations of stochastically interacting particles. ``Noisy'' sums with fluctuations proportional to 1/ {}n , where n is the number of particles in the simulation, provide feedback that drives the instability. Numerical illustrations of an energy loss or ``cooling'' instability in an Ornstein-Uhlenbeck process support our analysis.